Craps dice probability
Dice probability for every roll, combination by combination
Pick any total from 2 to 12 and see exactly which two-dice combinations make it, its true probability, and the place, hardway or hop bet odds that go with that number.
Every figure here comes from the 36 equally likely outcomes of rolling two fair six-sided dice.
Rolling a 6 with two dice
5 of 36 combinations · 13.89%
31 to 5 against. The combinations that make this total: ⚀⚄ ⚄⚀ ⚁⚃ ⚃⚁ ⚂⚂
Place bet (wins if 6 rolls before a 7): pays 7:6, house edge 1.52%.
Hardway bet (wins if 6 rolls as a double, 3-3, before a 7 or an 'easy' 6): pays 9:1, house edge 9.09%.
Hop bet on the hard combo (single roll only): pays 30:1, house edge 13.89%.
Why are there 36 combinations with two dice?
Roll two dice and there are 6 possible faces on each, giving 6 × 6 = 36 equally likely combinations in total. Those 36 combinations only add up to 11 different totals (2 through 12), but they don't spread evenly across them, some totals have far more ways to appear than others. That uneven spread is the entire reason a craps table pays 4 and 10 far better than it pays 6 and 8, and it's worth internalising before any bet on the table makes intuitive sense.
| Total | Combinations | Ways | Probability |
|---|---|---|---|
| 2 | 1-1 | 1 | 2.78% |
| 3 | 1-2, 2-1 | 2 | 5.56% |
| 4 | 1-3, 3-1, 2-2 | 3 | 8.33% |
| 5 | 1-4, 4-1, 2-3, 3-2 | 4 | 11.11% |
| 6 | 1-5, 5-1, 2-4, 4-2, 3-3 | 5 | 13.89% |
| 7 | 1-6, 6-1, 2-5, 5-2, 3-4, 4-3 | 6 | 16.67% |
| 8 | 2-6, 6-2, 3-5, 5-3, 4-4 | 5 | 13.89% |
| 9 | 3-6, 6-3, 4-5, 5-4 | 4 | 11.11% |
| 10 | 4-6, 6-4, 5-5 | 3 | 8.33% |
| 11 | 5-6, 6-5 | 2 | 5.56% |
| 12 | 6-6 | 1 | 2.78% |
What is the difference between a hardway and a hop bet?
A hardway bet stays live over several rolls until it wins or loses, while a hop bet is settled on the very next roll. That's why a "hard 6" bet and a hop on 3-3 pay differently, even though both need the same dice. The difference is entirely in how long the bet stays live. A hardway bet rides across every roll until it's resolved one way or the other, either the double you want shows up, the 7 shows up, or that number lands the "easy" way with different dice, any one of those three ends the bet. A hop bet only gets one shot, the very next roll and nothing more. Because a hardway bet gets multiple chances to win before it can lose, its true odds are noticeably better for the player than a single-roll hop on the identical combination, which the payouts above reflect once you toggle between the two on any of 4, 6, 8 or 10.
Why is there no hardway bet on 5 or 9?
This one trips people up: 5 and 9 simply don't have a hardway option on the layout. A double can only ever land on an even total (1-1, 2-2, 3-3, 4-4, 5-5 or 6-6, giving 2, 4, 6, 8, 10 or 12), so there's no matching-dice way to make an odd total like 5 or 9 in the first place. Select either number above and the tool shows the only real single-roll alternative, hopping one of its specific combinations directly.
The same 36 combinations, everywhere
These are the same 36 combinations behind every figure on the Craps AI hub calculator, and behind why free odds bets pay exactly what they pay on the odds calculator. None of it changes shooter to shooter or casino to casino, which is exactly why no AI system, prediction app or "hot dice" streak can shift these numbers, they're fixed by simple arithmetic on a fair pair of dice. One more number from that arithmetic: because a 7 can appear on any roll, the average shooter's hand lasts just 8.53 rolls before sevening out.
Spotting the bad bets
Knowing the 36 combinations makes the bad bets easy to spot.
FAQ
Dice probability FAQ
Why is 7 the most common craps roll?+
Because more combinations of two dice add up to 7 than any other total, six out of 36 possible rolls: 1-6, 6-1, 2-5, 5-2, 3-4 and 4-3. Every other total has fewer ways to make it, which is exactly why 7 is both the shooter's friend on the come-out roll and every point bettor's biggest threat afterwards.
What's the difference between a hardway bet and a hop bet?+
A hardway bet stays on the table across multiple rolls and wins whenever the chosen double, like 3-3 for a hard 6, appears before either a 7 or that number rolled the "easy" way. A hop bet resolves on the very next roll only, betting on one specific dice combination appearing immediately, which is why hop bets carry worse odds despite sometimes higher payouts.
Why don't 5 and 9 have hardway bets?+
Because neither total can be made with matching dice. A double can only ever produce an even total, 2, 4, 6, 8, 10 or 12, so there's no "hard" version of 5 or 9 to bet on, only the ordinary combinations like 2-3 or 4-5.
Are loaded or weighted dice used in real casinos?+
No, not in any licensed casino. Regulated casino dice are precision-milled to strict tolerances, transparent, sharp-edged and regularly inspected, specifically to rule out the kind of physical bias that would make one number more likely than the maths here predicts.
Can a computer or AI calculate loaded dice from past rolls?+
In principle, yes, statisticians and casino surveillance teams do run exactly this kind of analysis to catch defective dice, comparing observed roll frequencies against the expected ones shown here over a large enough sample. It has nothing to do with predicting a fair die's next roll, which stays impossible, it only flags dice that are already physically biased.
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